Modal structure of high power thin-disk vortex laser under thermal effect

Lian Tian-Hong; Dou Yi-Qun; Zhou Lei; Liu Yun; Kou Ke; Jiao Ming-Xing

doi:10.7498/aps.73.20240757

Abstract

Optical vortex beam has wide applications in areas of optical communication, lidar detection and optical trapping. To increase the operating distance, a high-power vortex laser source is necessary in these applications. However, the purity of the output vortex beam decreases with the pump power increasing due to the thermal effect of the laser medium. Therefore, modal field degeneration induced by thermal effect of laser medium has become a key problem in high-power vortex solid-state laser. To investigate this modal field degeneration, the heat transfer and thermal deformation model of an annular beam end pumped thin-disk vortex laser (Fig. (a)) is established. The phase difference of the thermal effect is calculated based on this model. Then, the quadratic term is separated from the phase difference. The non-quadratic term, as a small perturbation, is substituted into the diffraction integral equation of the laser cavity. The modal field structure is obtained by using the perturbation method. The variations of the modal structure with pump power, absorption coefficient and crystal thickness are investigated for three kinds of laser crystals, i.e. Nd:YAG, Nd:YLF and Nd:YVO₄. The results show that the modal field under thermal effect presents obvious deviation from the ideal mode at high power, and the modal structure shows that it contains many higher-order radial modes, with the angular mode order unchanged. Hence, the radial modal spectrum is broadened by the thermal effect. For an ideal vortex laser without thermal effect operating on the radial mode order 0 and angular mode order 1, Fig. (b) shows the modal structures with thermal effect under different pump power values with a laser crystal thickness of 1 mm. The ratio of the higher-order modes increases and the modal structure becomes more and more complex with the pump power increasing. The ratios of the ideal mode are 0.99, 0.97, 0.90, 0.79 and 0.61, under the pump power of 10 W, 20 W, 40 W, 60 W and 100 W, respectively. Moreover, the Nd:YVO₄ laser has the largest and the Nd:YAG laser has the smallest modal spectrum broadening under the same pump power. Figure (c) shows the variation of the modal purity with the pump power. The modal purity of the Nd:YVO₄ and the Nd:YLF laser decrease to 0.35 and 0.44 at the pump power of 100 W, respectively. We also investigate the modal structures under different absorption coefficients and crystal thickness values. A larger absorption coefficient or a smaller crystal thickness leads to a larger radial modal spectrum broadening and a smaller modal purity. These results indicate that in the design of high-power thin-disk vortex laser, it is necessary to comprehensively optimize the disk thickness and the absorption coefficient, and consider modal spectrum broadening as well.

Keywords:

Authors and contacts

School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology, Xi’an 710048, China

Corresponding author: Lian Tian-Hong, tianhongl@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61805196, 51875455).

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References

[1]	Wang J, Yang J Y, Fazal I M, et al. 2012 Nat. Photonics 6 488 Google Scholar
[2]	Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas’ko V, Barnett S M, Franke-Arnold S, 2004 Opt. Express 12 5448 Google Scholar
[3]	Willner A E, Zhao Z, Ren Y X, Li L, Xie G D, Song H Q, Liu C, Zhang R Z, Bao C J, Pang K 2018 Opt. Commun. 408 21 Google Scholar
[4]	Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 341 537 Google Scholar
[5]	Belmonte A, Rosales-Guzman C, Torres J P 2015 Optica 2 1002 Google Scholar
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[8]	Jantzi A, Jemison W, Laux A, Mullen L, Cochenour B 2018 Opt. Express 26 2668 Google Scholar
[9]	Baghdady J, Miller K, Morgan K, et al. 2016 Opt. Express 24 9794 Google Scholar
[10]	Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light Sci. Appl. 8 90 Google Scholar
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[12]	Forbes A 2019 Laser Photonics Rev. 13 1900140 Google Scholar
[13]	Forbes A, Oliveira M D, Dennis M R 2021 Nat. Photonics 15 253 Google Scholar
[14]	孙喜博, 朱启华, 刘兰琴, 黄晚晴, 张颖, 王文义, 耿远超 2017 激光与光电子学进展 54 070001 Google Scholar Sun X B, Zhu Q H, Liu L Q, Huang W Q, Zhang Y, Wang W Y, Geng Y C 2017 Laser Optoelectron. P. 54 070001 Google Scholar
[15]	付时尧, 高春清 2019 光学学报 39 0126014 Google Scholar Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014 Google Scholar
[16]	常宁, 金立伟, 高玮 2019 光学学报 39 0319001 Google Scholar Chang N, Jin L W, Gao W 2019 Acta Opt. Sin. 39 0319001 Google Scholar
[17]	Zhao Y G, Chen B, Zheng C S, Jia D W, Dong J F, Guo J, Wang Z X, Yu H H, Zhang H J 2024 Laser Photonics Rev. 18 2301089 Google Scholar
[18]	Pan J, Shen Y J, Wan Z S, Fu X, Zhang H K, Liu Q 2020 Phys. Rev. Appl. 14 044048 Google Scholar
[19]	Zhao Y G, Wang L, Chen W D, et al. 2021 Photonics Res. 9 357 Google Scholar
[20]	Qiao Z, Xie G Q, Wu Y H, Yuan P, Ma J G, Qian L J, Fan D Y 2018 Laser Photonics Rev. 12 1800019 Google Scholar
[21]	宋小鹿, 李兵斌, 王石语, 蔡德芳, 文建国, 过振 2008 红外与激光工程 37 73 Google Scholar Song X L, Li B B, Wang S Y, Cai D F, Wen J G, Guo Z 2008 Infrared Laser Eng. 37 73 Google Scholar
[22]	姚育成, 刘丹琳, 黄楚云, 徐国旺, 王贝 2016 光子学报 45 131 Google Scholar Yao Y C, Liu D L, Huang C Y, Xu G W, Wang B 2016 Acta Photonica Sin. 45 131 Google Scholar
[23]	方洪烈 2014 光学谐振腔与引力波探测 (北京: 科学出版社) 第78—80页 Fang H L 2014 Optical Resonators and Gravitational Wave Detection (Beijing: Science Press ) pp78–80
[24]	Koechner W 2013 Solid-State Laser Engineering (New York: Springer) pp46–83

Cited By

图 1 环形光端面泵浦薄片涡旋激光器结构

Figure 1. Schematic of an annular beam end pumped thin-disk vortex laser.

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图 2 Nd:YAG温度和热形变分布　(a)三维温度分布; (b)三维热形变分布; (c)剖面温度; (d)剖面形变

Figure 2. Temperature and thermal deformation of Nd:YAG crystal: (a) 3D temperature distribution; (b) 3D deformation distribution; (c) temperature in the section plane; (d) deformation in the section plane.

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图 3 不同泵浦功率下3种晶体的温度及热形变　(a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO₄温度; (f) Nd:YVO₄形变

Figure 3. Temperature and thermal deformation of the three laser crystals under different pump power: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO₄; (f) deformation of Nd:YVO₄.

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图 4 温度及热形变随泵浦功率的变化　(a) 最高温度; (b) 最高温度与中心温差; (c) 最大热形变; (d) 最大热形变与中心热形变差

Figure 4. Variation of temperature and thermal deformation with pump power: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.

DownLoad: Full-Size Img PowerPoint

图 5 不同泵浦功率下的模场分布和模谱结构　(a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO₄模场; (f) Nd:YVO₄模谱

Figure 5. Mode distribution and mode structure under different pump power: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO₄ mode distribution; (f) Nd:YVO₄ mode structure.

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图 6 模式纯净度随泵浦功率的变化

Figure 6. Variation of the modal purity with pump power.

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图 7 不同吸收系数下3种晶体的温度及形变　(a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO₄温度; (f) Nd:YVO₄形变

Figure 7. Temperature and deformation of the three laser crystals under different absorption coefficient: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO₄; (f) deformation of Nd:YVO₄.

DownLoad: Full-Size Img PowerPoint

图 8 温度及热形变随吸收系数的变化　(a) 最高温度; (b) 最高温度与中心温度差值; (c) 最大热形变; (d) 最大热形变与中心热形变差值

Figure 8. Variation of temperature and thermal deformation with absorption coefficient: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.

DownLoad: Full-Size Img PowerPoint

图 9 不同吸收系数下的模场分布和模谱结构　(a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO₄模场; (f) Nd:YVO₄模谱

Figure 9. Mode distribution and mode structure under different absorption coefficient: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO₄ mode distribution; (f) Nd:YVO₄ mode structure.

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图 10 模式纯净度随吸收系数的变化

Figure 10. Variation of the modal purity with absorption coefficient.

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图 11 不同厚度下3种晶体的温度及热形变　(a) Nd:YAG温度; (b) Nd:YAG形变; (c) Nd:YLF温度; (d) Nd:YLF形变; (e) Nd:YVO₄温度; (f) Nd:YVO₄形变

Figure 11. Temperature and thermal deformation of the three laser crystals under different crystal thickness: (a) Temperature of Nd:YAG; (b) deformation of Nd:YAG; (c) temperature of Nd:YLF; (d) deformation of Nd:YLF; (e) temperature of Nd:YVO₄; (f) deformation of Nd:YVO₄.

DownLoad: Full-Size Img PowerPoint

图 12 温度及热形变随晶体厚度的变化　(a) 最高温度; (b) 最高温度与中心温度差值; (c) 最大热形变; (d) 最大热形变与中心热形变差值

Figure 12. Variation of temperature and thermal deformation with crystal thickness: (a) Maximum temperature; (b) difference between the maximum temperature and the center temperature; (c) maximum thermal deformation; (d) difference between the maximum thermal deformation and the center thermal deformation.

DownLoad: Full-Size Img PowerPoint

图 13 不同厚度下的模场分布和模谱结构　(a) Nd:YAG模场; (b) Nd:YAG模谱; (c) Nd:YLF模场; (d) Nd:YLF模谱; (e) Nd:YVO₄模场; (f) Nd:YVO₄模谱

Figure 13. Mode distribution and mode structure under different thickness: (a) Nd:YAG mode distribution; (b) Nd:YAG mode structure; (c) Nd:YLF mode distribution; (d) Nd:YLF mode structure; (e) Nd:YVO₄ mode distribution; (f) Nd:YVO₄ mode structure.

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图 14 模式纯净度随晶体厚度的变化

Figure 14. Variation of modal purity with crystal thickness.

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表 1 激光晶体参数^[24]

Table 1. Parameters of laser crystals^[24].

激光晶体	密度/ (kg·m^–3)	杨氏模量/GPa	泊松比	热膨胀系数/K^–1	热导率/ (W·m^–1·K^–1)	$ {{{\text{d}}n} \mathord{\left/ {\vphantom {{{\text{d}}n} {{\text{d}}T}}} \right. } {{\text{d}}T}} $/K^–1
Nd:YAG	4560	317	0.25	7.5×10⁶	14	7.3×10^–6
Nd:YLF	3990	85	0.33	8.3×10⁶	6.3	–6.6×10^–6
Nd:YVO₄	4220	133	0.33	4.43×10⁶	5.2	8.5×10^–6

DownLoad: CSV

[1]	Wang J, Yang J Y, Fazal I M, et al. 2012 Nat. Photonics 6 488 Google Scholar
[2]	Gibson G, Courtial J, Padgett M J, Vasnetsov M, Pas’ko V, Barnett S M, Franke-Arnold S, 2004 Opt. Express 12 5448 Google Scholar
[3]	Willner A E, Zhao Z, Ren Y X, Li L, Xie G D, Song H Q, Liu C, Zhang R Z, Bao C J, Pang K 2018 Opt. Commun. 408 21 Google Scholar
[4]	Lavery M P J, Speirits F C, Barnett S M, Padgett M J 2013 Science 341 537 Google Scholar
[5]	Belmonte A, Rosales-Guzman C, Torres J P 2015 Optica 2 1002 Google Scholar
[6]	杨伟东, 邱晓东, 陈理想 2020 中国激光 47 0500013 Google Scholar Yang W D, Qiu X D, Chen L X 2020 Chin. J. Lasers 47 0500013 Google Scholar
[7]	杨苏辉, 廖英琦, 林学彤, 刘欣宇, 齐若伊, 郝燕 2021 红外与激光工程 50 20211040 Google Scholar Yang S H, Liao Y Q, Lin X T, Liu X Y, Qi R Y, Hao Y 2021 Infrared Laser Eng. 50 20211040 Google Scholar
[8]	Jantzi A, Jemison W, Laux A, Mullen L, Cochenour B 2018 Opt. Express 26 2668 Google Scholar
[9]	Baghdady J, Miller K, Morgan K, et al. 2016 Opt. Express 24 9794 Google Scholar
[10]	Shen Y J, Wang X J, Xie Z W, Min C J, Fu X, Liu Q, Gong M L, Yuan X C 2019 Light Sci. Appl. 8 90 Google Scholar
[11]	柳强, 潘婧, 万震松, 申艺杰, 张恒康, 付星, 巩马理 2020 中国激光 47 0500006 Google Scholar Liu Q, Pan J, Wan Z S, Shen Y J, Zhang H K, Fu X, Gong M L 2020 Chin. J. Lasers 47 0500006 Google Scholar
[12]	Forbes A 2019 Laser Photonics Rev. 13 1900140 Google Scholar
[13]	Forbes A, Oliveira M D, Dennis M R 2021 Nat. Photonics 15 253 Google Scholar
[14]	孙喜博, 朱启华, 刘兰琴, 黄晚晴, 张颖, 王文义, 耿远超 2017 激光与光电子学进展 54 070001 Google Scholar Sun X B, Zhu Q H, Liu L Q, Huang W Q, Zhang Y, Wang W Y, Geng Y C 2017 Laser Optoelectron. P. 54 070001 Google Scholar
[15]	付时尧, 高春清 2019 光学学报 39 0126014 Google Scholar Fu S Y, Gao C Q 2019 Acta Opt. Sin. 39 0126014 Google Scholar
[16]	常宁, 金立伟, 高玮 2019 光学学报 39 0319001 Google Scholar Chang N, Jin L W, Gao W 2019 Acta Opt. Sin. 39 0319001 Google Scholar
[17]	Zhao Y G, Chen B, Zheng C S, Jia D W, Dong J F, Guo J, Wang Z X, Yu H H, Zhang H J 2024 Laser Photonics Rev. 18 2301089 Google Scholar
[18]	Pan J, Shen Y J, Wan Z S, Fu X, Zhang H K, Liu Q 2020 Phys. Rev. Appl. 14 044048 Google Scholar
[19]	Zhao Y G, Wang L, Chen W D, et al. 2021 Photonics Res. 9 357 Google Scholar
[20]	Qiao Z, Xie G Q, Wu Y H, Yuan P, Ma J G, Qian L J, Fan D Y 2018 Laser Photonics Rev. 12 1800019 Google Scholar
[21]	宋小鹿, 李兵斌, 王石语, 蔡德芳, 文建国, 过振 2008 红外与激光工程 37 73 Google Scholar Song X L, Li B B, Wang S Y, Cai D F, Wen J G, Guo Z 2008 Infrared Laser Eng. 37 73 Google Scholar
[22]	姚育成, 刘丹琳, 黄楚云, 徐国旺, 王贝 2016 光子学报 45 131 Google Scholar Yao Y C, Liu D L, Huang C Y, Xu G W, Wang B 2016 Acta Photonica Sin. 45 131 Google Scholar
[23]	方洪烈 2014 光学谐振腔与引力波探测 (北京: 科学出版社) 第78—80页 Fang H L 2014 Optical Resonators and Gravitational Wave Detection (Beijing: Science Press ) pp78–80
[24]	Koechner W 2013 Solid-State Laser Engineering (New York: Springer) pp46–83

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